### Abstract

For n independent, identically distributed uniform points in [0, 1]^{d}, d ≥ 2, let L_{n} be the total distance from the origin to all the minimal points under the coordinatewise partial order (this is also the total length of the rooted edges of a minimal directed spanning tree on the given random points). For d ≥ 3, we establish the asymptotics of the mean and the variance of L_{n}, and show that L_{n} satisfies a central limit theorem, unlike in the case d = 2.

Original language | English |
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Pages (from-to) | 1-30 |

Number of pages | 30 |

Journal | Advances in Applied Probability |

Volume | 38 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2006 Mar 1 |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Applied Mathematics

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## Cite this

Bai, Z. D., Lee, S., & Penrose, M. D. (2006). Rooted edges of a minimal directed spanning tree on random points.

*Advances in Applied Probability*,*38*(1), 1-30. https://doi.org/10.1239/aap/1143936137